# Why doesn't pressure depend on the shape of the container?

Frigus
As we know that liquids(same) at same height exert same pressure because of height difference but as I have a question in which there are some figures In which the (d) part lower part is extended horizontally,so by common sense the pressure in horizontal direction should increase But why at that level(horizontal) pressure increases from all sides?

Please try to tell me verbally not by proving it mathematically.

<< Mentor Note -- Two similar threads merged into this one >>

Last edited by a moderator:

Mentor
As we know that liquids(same) at same height exert same pressure because of height difference but as I have a question in which there are some figures In which the (d) part lower part is extended horizontally,so by common sense the pressure in horizontal direction should increase But why at that level(horizontal) pressure increases from all sides?

Please try to tell me verbally not by proving it mathematically.

View attachment 250530
The pressure at a given depth is a function solely of the depth of the fluid. Extending the container horizontally has no effect on the pressure. In figure d, at every point on the lower dotted line the pressure is the same.

..., so by common sense ...

sepcurio
The pressure spreads out throughout the liquid. The more liquid there is, the more force there is; but also, the more liquid there is, the more room there is for the force to spread out. So it always balances out no matter how much liquid you have.

Because it spreads out throughout, it doesn't matter what shape the container is.

russ_watters
Frigus
The pressure in liquid is because of water coloum above the surface but there is no water coloum above a point in lower horizontal tube part in figure(d) on left hand side but why at any point in lower horizontal tube part has same pressure as that of other tubes.

Last edited by a moderator:
2022 Award
Push the end of the tube in a little bit. What happens to the water level at the top of the tube?

If you stop pushing at the end of the tube, what happens to the end of the tube? What happens to the water level?

Frigus
Push the end of the tube in a little bit. What happens to the water level at the top of the tube?

If you stop pushing at the end of the tube, what happens to the end of the tube? What happens to the water level?

I understand the thing you want to say but I want to know from where the pressure in upward side will generated.

2022 Award
I understand the thing you want to say but I want to know from where the pressure in upward side will generated.
On the upward side of what? The horizontal bit of the tube? It comes from the water in the horizontal bit stopping the water in the vertical bit from flowing downwards into the horizontal bit.

Frigus
On the upward side of what? The horizontal bit of the tube? It comes from the water in the horizontal bit stopping the water in the vertical bit from flowing downwards into the horizontal bit.
On the upward side of what? The horizontal bit of the tube? It comes from the water in the horizontal bit stopping the water in the vertical bit from flowing downwards into the horizontal bit.
I am talking about a point on lower horizontal portion of L tube in d figure which can lie anywhere on left hand side to the point where both the horizontal and vertical part of tube meets.

2022 Award
I am talking about a point on lower horizontal portion of L tube in d figure which can lie anywhere on left hand side to the point where both the horizontal and vertical part of tube meets.
Like I said - the tube stops the water in the horizontal section from flowing away, which stops the water in the vertical section from flowing down. Hence the pressure.

russ_watters
Homework Helper
I want to know from where the pressure in upward side will generated.
You might want to consider abandoning the cause-effect mind set. It is better to embrace the relationships and equations which exist without trying to understand them all in terms of cause and effect.

One difficulty with cause-effect reasoning is that the network of causes and effects is very broad. At the bottom, almost everything is interwoven with everything else. In the case of Pascal's principle, the best causal explanation I can offer involves the notion of relaxation toward an equilibrium state.

Suppose that we start with a fluid that is in an equilibrium state. For instance, there is a syringe upright in the doctor's hand. His thumb is on the plunger but not pressing down. There is some wax stuck to the tip of the needle so that no fluid can escape. The doctor presses on the plunger. This is the cause. Now what happens? The complicated answer is that the motion of the thumb creates stress where the thumb meets the plunger. The end of the plunger deforms under that stress. This produces a strain that propagates through the plunger until the whole thing moves very slightly into the fluid. This stress on the fluid produces a small deflection and increased pressure locally within the fluid. This produces a pressure wave within the fluid. Meanwhile, becauase the density of the fluid and the density of the plunger do not match, a portion of the pressure wave in the plunger is reflected back up toward the doctor's thumb... mumble, mumble, mumble, ... who cares?

Eventually the system reaches a new equilibrium about which we can reason.

Frigus
You might want to consider abandoning the cause-effect mind set. It is better to embrace the relationships and equations which exist without trying to understand them all in terms of cause and effect.

One difficulty with cause-effect reasoning is that the network of causes and effects is very broad. At the bottom, almost everything is interwoven with everything else. In the case of Pascal's principle, the best causal explanation I can offer involves the notion of relaxation toward an equilibrium state.

Suppose that we start with a fluid that is in an equilibrium state. For instance, there is a syringe upright in the doctor's hand. His thumb is on the plunger but not pressing down. There is some wax stuck to the tip of the needle so that no fluid can escape. The doctor presses on the plunger. This is the cause. Now what happens? The complicated answer is that the motion of the thumb creates stress where the thumb meets the plunger. The end of the plunger deforms under that stress. This produces a strain that propagates through the plunger until the whole thing moves very slightly into the fluid. This stress on the fluid produces a small deflection and increased pressure locally within the fluid. This produces a pressure wave within the fluid. Meanwhile, becauase the density of the fluid and the density of the plunger do not match, a portion of the pressure wave in the plunger is reflected back up toward the doctor's thumb... mumble, mumble, mumble, ... who cares?

Eventually the system reaches a new equilibrium about which we can reason.

Sir I became a great fan of yours, I jointed one day ago and I got a best teacher which know my mindset just by reading my questions.

sir I understand that a pressure is generated in horizontal direction from your explanation but I want to know why a perpendicular pressure is generated to the syringe .

Homework Helper
sir I understand that a pressure is generated in horizontal direction from your explanation but I want to know why a perpendicular pressure is generated to the syringe .
Because it can not be otherwise if an equilibrium is to exist.

Frigus
Because it can not be otherwise if an equilibrium is to exist.
Sir I can't understand what you want to say.

I want to say that a when we apply a pressure(vertically) in tube why a force perpendicular to the tube means in horizontal direction is generated.

Homework Helper
I want to say that a when we apply a pressure(vertically) in tube why a force perpendicular to the tube means in horizontal direction is generated.
The applicable remark was "it cannot be otherwise if an equilibrum is to exist".

Assume that an equilibrium exists. That is, assume that every tiny volume in the fluid is at rest and is unaccelerated by its interactions with all the other tiny volumes.

Now suppose (for purposes of a proof by contradiction) that we have a small parcel of fluid that is subject to a vertical pressure from both top and bottom but no horizontal pressure from the sides. What happens next?

Answer: that small parcel of fluid will be compressed from top and bottom and will squish out to the sides.

But that violates the equilibrium assumption. Contradiction. Which means that our supposition was false. The pressure on that parcel must be equal on all sides.

gleem and russ_watters
Frigus
The applicable remark was "it cannot be otherwise if an equilibrum is to exist".

Assume that an equilibrium exists. That is, assume that every tiny volume in the fluid is at rest and is unaccelerated by its interactions with all the other tiny volumes.

Now suppose (for purposes of a proof by contradiction) that we have a small parcel of fluid that is subject to a vertical pressure from both top and bottom but no horizontal pressure from the sides. What happens next?

Answer: that small parcel of fluid will be compressed from top and bottom and will squish out to the sides.

But that violates the equilibrium assumption. Contradiction. Which means that our supposition was false. The pressure on that parcel must be equal on all sides.
Thanks a lot sir 😊

Mentor
The pressure spreads out throughout the liquid. The more liquid there is, the more force there is; but also, the more liquid there is, the more room there is for the force to spread out. So it always balances out no matter how much liquid you have.

Because it spreads out throughout, it doesn't matter what shape the container is.
Most of what you wrote is at best, unclear and sloppy, and at worst, just plain wrong.
"pressure spreads out throughout the liquid" -- no, the pressure at a given depth is the same at each point at that depth.

"the more liquid there is, the more force there is, the more room there is for the force to spread out" -- is wrong. Referring to the image in post #1, the pressure at depth h (in units of, say, lb/in^2), is the same in all four containers. Note that the pressure involves a force and an area. A container with more liquid does not exert more force per unit area than one with less liquid.

"So it always balances out no matter how much liquid you have." -- what balances out? If there is a greater force per unit area, when there is more liquid, as you claimed, that's equivalent to saying that the pressure is greater when there is more liquid, which is not true.

sepcurio
Mark44 said:

Most of what you wrote is at best, unclear and sloppy, and at worst, just plain wrong.
"pressure spreads out throughout the liquid" -- no, the pressure at a given depth is the same at each point at that depth.

I didn't say that the pressure was the same throughout the liquid, I said that it spreads out throughout the liquid.

"the more liquid there is, the more force there is, the more room there is for the force to spread out" -- is wrong. Referring to the image in post #1, the pressure at depth h (in units of, say, lb/in^2), is the same in all four containers. Note that the pressure involves a force and an area. A container with more liquid does not exert more force per unit area than one with less liquid.

I'm afraid you've misquoted me. I said, "the more liquid there is, the more room there is for the force to spread out"

"So it always balances out no matter how much liquid you have." -- what balances out? If there is a greater force per unit area, when there is more liquid, as you claimed, that's equivalent to saying that the pressure is greater when there is more liquid, which is not true.

Again, you misrepresented what I said. I did not say that there is a greater force per unit area. When you use the phrase, "force per unit area", that's math expressed with words. The OP specifically requested a simple answer without math. I phrased the answer in as simple language as I could without using math (either linguistically or numerically/symbolically).

The OP seemed like he was really stuck on this concept. My intent was not to be precise, but to provide exposition that could guide the OP's understanding to an epiphany so he could get "unstuck" and continue learning about the subject.

Thank you for the feedback.

Last edited:
Gold Member
no, the pressure at a given depth is the same at each point at that depth.
This is true but taking the experiment up into space, initially, could perhaps help. The only pressure throughout the liquid in a syringe will be due to the piston and it will be the same everywhere. The pressure against all the walls and the piston will all be the same and the same as the pressure everywhere inside the liquid, measured in any direction with a tiny pressure meter.
Once you go to ground level, there will be a contribution from gravity, which increases with depth but over any horizontal section at a given depth, the same pressure will also act in all directions - including upwards against a horizontal surface.

Mentor
I didn't say that the pressure was the same throughout the liquid, I said that it spreads out throughout the liquid.
So does the pressure spread out uniformly? "Spreading out throughout the liquid" is too vague to be very helpful, considering the containers shown in the image of post #1.
sepcurio said:
I'm afraid you've misquoted me. I said, "the more liquid there is, the more room there is for the force to spread out"
You're right. I didn't quote your exact words, but my misquote wasn't too far from what you wrote.. Here are your exact words.
The more liquid there is, the more force there is; but also, the more liquid there is, the more room there is for the force to spread out.

How is this helpful to the OP in light of the image he posted, and considering that he asked about the pressure at level h in the four containers? IMO, your description is not helpful at all.

sepcurio said:
Again, you misrepresented what I said. I did not say that there is a greater force per unit area. When you use the phrase, "force per unit area", that's math expressed with words.
No, that's not math -- it's how the term "pressure" is defined. If we're talking about pressure and force, we have to distinguish between the two -- where one is a force and one is a force acting on a unit area. This is all the more important in this thread as I don't believe the OP is clear on the difference.
sepcurio said:
The OP specifically requested a simple answer without math. I phrased the answer in as simple language as I could without using math (either linguistically or numerically/symbolically).
Someone said a long time ago (Einstein?) -- "Make things as simple as possible, but no simpler. Providing an answer without a clear distinction between the difference between a force being applied and the resulting pressure oversimplifies things, IMO.

Frigus
The pressure at a given depth is a function solely of the depth of the fluid. Extending the container horizontally has no effect on the pressure. In figure d, at every point on the lower dotted line the pressure is the same.

Why

Ok sir I will work on it
As we know that liquids(same) at same height exert same pressure because of height difference but as I have a question in which there are some figures In which the (d) part lower part is extended horizontally,so by common sense the pressure in horizontal direction should increase But why at that level(horizontal) pressure increases from all sides?

Please try to tell me verbally not by proving it mathematically.

<< Mentor Note -- Two similar threads merged into this one >>

View attachment 250530

Can anyone also explain me this case,

If we create a pressure in liquid by pushing the piston in given figure a same pressure will be developed in height a and b a irrespective of their area please tell me why a same pressure propagates.

Last edited by a moderator:
Mentor
Why

Ok sir I will work on it

Can anyone also explain me this case,

If we create a pressure in liquid by pushing the piston in given figure a same pressure will be developed in height a and b a irrespective of their area please tell me why a same pressure propagates.
Post #15 is still an excellent answer. Changing the example doesn't change the basic principles. Can you explain what it is about post #15 you don't understand?

Gunnir
Have a think about it this way Hemant...

Think about helium in a balloon; what shape does this balloon want to be? Spherical, no? In real life it isn't always exactly spherical because a number of different effects. Importantly however, it *wants* be spherical. It *wants* to create a shape which is exerting a force equally on every unit of the surface of the shape...

So now let's stop that, let's force that balloon into a, umm... a large funnel... What happens to the surface of the top of the balloon as we force it in? Does it stay the same? Or does it start to expand outwards into free space?

That right there is key to understanding this. When you force the balloon to have a partially conical shape (using the funnel), the physically unrestricted region of the balloon will expand into free space; the balloon is trying to maintain constant pressure by doing work on the balloon material. If we pretend it cost no energy to expand the balloon surface, pressure would stay exactly the same right? I'm just moving the same volume and mass of helium around in different places - and it freely expands to retain constant pressure regardless of the shape of the vessel.

I hope based off your quote in #22, that helps a bit?

Mentor
The pressure at a given depth is a function solely of the depth of the fluid. Extending the container horizontally has no effect on the pressure. In figure d, at every point on the lower dotted line the pressure is the same.
Why
I explained why in the first sentence of what I wrote way back in post #2. I have copied it to this post, with the explanation in bold.
Can anyone also explain me this case,

If we create a pressure in liquid by pushing the piston in given figure a same pressure will be developed in height a and b a irrespective of their area please tell me why a same pressure propagates.
There is an important difference between the image of the four containers in post #1, and the image of the funnel shaped container in post #21. The containers shown in post #1 are all open at the top, so the weight of the air in the atmosphere above each container is pressing down on the top layer of the liquid in the container. The pressure at the top layer of the liquid is about 14.7 lb/in^2. At lower levels in each container, there is also the additional weight of the liquid above, so the pressure is higher at lower horizontal levels (i.e., for larger values of h). For container d, with a horizontal extension, it doesn't matter how far horizontally that extension goes -- all points at the same horizontal level have the same height of fluid and the same column of atmospheric air pressing on them, so the pressure is the same at each point that is h units below the top of the liquid.

The container in post #21 is different, because it is closed at the top, so the air in the atmosphere is not pressing down on the top layer of fluid. Let's say that you start the experiment by turning the container over and filling it with fluid, and then inserting the piston so that there is no air between the piston and fluid. Now turn the container again so that the piston is at the bottom. At this time, because of atmospheric pressure on the outer end of the piston, the pressure inside the container will be the same as atmospheric pressure, about 14.7 lb/in^2.

If you push on the piston, you're squeezing the molecules of liquid near the piston. These molecules in turn push against other molecules higher up until all of the fluid in the container reaches the same, higher pressure. When you apply a force on the piston, which has a certain cross-sectional area, you're increasing the pressure on the liquid in the container, and that pressure propagates to all points, and all levels of that container. In this case, because the container is closed, it's not possible for the pressure to be greater at some places than at others.

Frigus
IM feeling that I am irritating great mentors by continuously asking questions but I am in very confused so I to
As we know that liquids(same) at same height exert same pressure because of height difference but as I have a question in which there are some figures In which the (d) part lower part is extended horizontally,so by common sense the pressure in horizontal direction should increase But why at that level(horizontal) pressure increases from all sides?

Please try to tell me verbally not by proving it mathematically.

<< Mentor Note -- Two similar threads merged into this one >>

View attachment 250530

Sir I want to know that when a pressure wave is generated by Piston in fluid why their is no change in pressure wave as it propagates though fluid.

Last edited by a moderator:
Homework Helper
Sir I want to know that when a pressure wave is generated by Piston in fluid why their is no change in pressure wave as it propagates though fluid.
Pascal's principle has to do with hydrostatics -- no transient pressures, no accelerations, no fluid flows. Everything is static.

The words you use above, "pressure wave" apply to hydrodynamics. There are transient pressures, accelerations and flows.

Pressure waves can and do change over time and space as they propagate through a fluid. Static pressure, by definition, does not change over time and does not change along a horizontal line.

After the disturbance produced by a piston's sudden motion has died away and everything has settled into a new equilibrium, one can look at the pressure along a horizontal line and find that it is the same all along it. That has very little to do with the transient behavior while the system was settling into its new equilibrium and everything to do with the conditions required for the new equilibrium to exist.

Last edited:
vanhees71, Delta2 and russ_watters
Gold Member
This was pointed out to the OP in his other thread:
OPs have a habit of moving the goal posts, rather than sorting out one thing at a time. But limiting the discussion to the final steady state of a system is more difficult than one might imagine. We often tend to bring in some unstated baggage in attempts to get understanding. Examples are deriving Electronic Feedback equations, Currents and Volts in a resistor network where the "how does it know" question can be a stumbling block. The approach can appear suspect to those who are unfamiliar with it.

Frigus
As we know that liquids(same) at same height exert same pressure because of height difference but as I have a question in which there are some figures In which the (d) part lower part is extended horizontally,so by common sense the pressure in horizontal direction should increase But why at that level(horizontal) pressure increases from all sides?

Please try to tell me verbally not by proving it mathematically.

<< Mentor Note -- Two similar threads merged into this one >>

View attachment 250530

Thanks a lot to all of you for cooperating with me, I am thankful to all

And finally I understood the pascal principle by reading again and again, thanks to all.